Advanced Math · Level 2

2.2 Integral Calculus

Take the next step on the calculus journey with integrals and sums.

Calculating Distance

Using Riemann Sums

The Definite Integral

First Calculations

The Fundamental Theorem of Calculus

Integrating Polynomials


Exponentials and Trig

Integration by Parts

Basics of Partial Fractions

Trigonometric Integrals

Trig Substitution

Integration in the World

Area and Probability

Calculating Volume

Arc Length and Surface Area

Integration in Physics I

Application: Differential Equations

Integration in Physics II

Zeno's Paradox & Sums

Sums and Sigma Notation

Secret Identities

Converging Sums

Ratio and Root Tests

The Integral Test

Rearrangements: 0=1?

Limit Comparison Test

Power Series

Basics of Fourier Series

Course description

In a sense, differential calculus is local: it focuses on aspects of a function near a given point, like its rate of change there. Integral calculus complements this by taking a more complete view of a function throughout part or all of its domain. This course provides complete coverage of the two essential pillars of integral calculus: integrals and infinite series. By the end, you'll know their core principles and how to apply them to problems in geometry, probability, and physics.

Topics covered

  • Applications of infinite sums
  • Applications of integrals
  • Convergence tests
  • Integration by parts
  • Partial fractions
  • Polynomial integrals
  • Power series
  • Riemann sums
  • Substitution rule
  • The Fundamental Theorem
  • Transcendental integrals
  • Trigonometric integrals

Prerequisites and next steps

You’ll need an understanding of algebra and the basics of functions, such as domain and range, graphs, and intercepts. You should also be familiar with exponential functions, logarithms, and basic trigonometric identities. A strong understanding of differential calculus is a must.


  • Calculus Fundamentals

Up next

Advanced Math · Level 3

3.1 Multivariable Functions

Discover the multi-dimensional space of multivariable functions, and learn how to think about scenarios with more than one changing parameter.

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